Related papers: Tables of record gaps between prime constellations

We have identified a previously unrecognized population of very compact, embedded low-mass Galactic stellar clusters. These tight (r$ \approx $0.14 pc) groupings appear as bright singular objects at the few arcsec resolution of the Spitzer…

Giant, wide-separation planets often lie in the gap between multiple, distinct rings of circumstellar debris: this is the case for the HR\,8799 and HD\,95086 systems, and even the solar system where the Asteroid and Kuiper belts enclose the…

One field of particular interest in Number Theory concerns the gaps between consecutive primes. Within the last few years, very important results have been achieved on how small these gaps can be. The strongest of these results were…

We have analyzed HCN(1-0) and CS(2-1) line profiles obtained with high signal-to-noise ratios toward distinct positions in three selected objects in order to search for small-scale structure in molecular cloud cores associated with regions…

This is an expository article on the recent marvellous theorem of Goldston, Pintz, and Yildirim on small gaps between prime numbers.

We give upper and lower bounds on the number of graphs of fixed degree which have a positive density of triangles. In particular, we show that there are very few such graphs, when compared to the number of graphs without this restriction.…

Some of the most massive globular clusters of our Milky Way, such as for example omega-Centauri, show a mixture of stellar populations spanning a few Gyr in age and 1.5 dex in metallicities. In contrast, standard formation scenarios predict…

We define a new class of sets -- stable sets -- of primes in number fields. For example, Chebotarev sets $P_{M/K}(\sigma)$, with $M/K$ Galois and $\sigma \in \Gal(M/K)$, are very often stable. These sets have positive (but arbitrary small)…

We have bandmerged candidate transiting planetary systems (from the Kepler satellite) and confirmed transiting planetary systems (from the literature) with the recent Wide-field Infrared Survey Explorer (WISE) preliminary release catalog.…

We study the distribution of the maximum gap size in one-dimensional hard-core models. First, we randomly sequentially pack rods of length $2$ onto an interval of length $L$, subject to the hard-core constraint that rods do not overlap. We…

Recent detailed observations of protoplanetary discs revealed a lot of sub-structures which are mostly ring-like. One interpretation is that these rings are caused by growing planets. These potential planets are not yet opening very deep…

Any $n$-tuple of points in the plane can be moved to any other $n$-tuple by a continuous motion with at most $\binom{n}{3}$ intermediate changes of the order type. Even for tuples with the same order type, the cubic bound is sharp: there…

We re-examine the recent suggestion of a high fraction of transition discs (i.e. those with a cleared inner hole) in M stars, motivated by the fact that we expect that, for M stars, even discs without inner holes should exhibit very weak…

The main asteroid belt lies between the orbits of Mars and Jupiter, but the region is not uniformly filled with asteroids. There are gaps, known as the Kirkwood gaps, in the asteroid distribution in distinct locations that are associated…

We bring to bear an empirical model of the distribution of twin primes and produce two distinct results. The first is that we can make a quantitative probabilistic prediction of the occurrence of gaps in the sequence of twins within the…

We consider seven distant galaxies with clearly evident spiral structure from HST images. Three of these were chosen from Vogt et al. (1996) (VFP) and have measured rotational velocities. Five were chosen from the Medium Deep Survey and are…

Clusters of galaxies are merging during the formation of large-scale structures in the Universe. Based on optical survey data, we identify a large sample of pre-mergers of galaxy clusters and merging subclusters in rich clusters. We find…

We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length $y$ around $x$, where $y\ll (\log x)^2$. In particular we conjecture that the maximum grows surprisingly slowly as $y$…

We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are…

Exoplanet surveys like Kepler, TESS, and K2 have shown that planetary systems are common in our galaxy. These surveys, along with several others, have identified thousands of planetary candidates, with more than five thousand having already…